Just bought another two 'Anglepoise' type lamps in Ikea yesterday. They have one advantage in that the springs seem to be set for the new low energy bulbs which weigh more than old fashioned bulbs and can cause drooping. The disadvantage is that they are not protected from the ingress of sawdust so you need to think about where they are going to be placed and keep an eye on any build up of dust. At eight pound odd as opposed to £40-£50 for a proper low voltage worklight they win hands down for an amateur, not sure an H&S inspector would like them in a pro shop though.
It uses a narrow, long flourescent twin tube in a head which is lined with a reflective material. I've had mine in use for years as a clamp-on office desk lamp (I'm pretty certain it is the same model to that in the picture, or very similar). I recently promoted it to use on my workbench.
On my one, the clamp-on base can be separated from the upper parts (angle-arms and lamp). I used this to advantage by making a new wooden base which can be plugged into any of the 19mm dog-holes in the bench top. It usually sits in one of the rear dog-holes in the area of the front vice, but it can be moved to any convenient location on the bench.
I was recently prompted to set this up to get better close-up lighting over a saw vice (one of the scenarios you mention).
It isn't super-counterbalanced like a real anglepoise - it's a lightweight construction and simply relies on thumbscrews & friction to hold the arms in the desired orientation - but what do you expect for £14?
I'd be happy to recommend the Arod: http://www.ikea.com/gb/en/catalog/products/80148700/ which is a really solid bit of kit. A somewhat more significant investment at 40 quid but it's a proper workmanlike tool, failing that you could keep an eye out in charity shops or on eBay for a traditional old fashioned anglepoise.
I have an assortment of lamps including Anglepoises but for close up work I use a cheapo Clarke illuminated magnifying one.
A while back I bought a few small flexy stem lamps from Ikea, one type uses a 40w? Long life bulb which is a bit dim - the other slightly more expensive Halogen ones work really well. Not only that they have a clip so can be mounted in various ways.
I use a couple on my bandsaw and Unimat lathe.